## 1 Introduction  
The implementation of nanotechnology in real world applications relies on the use of accurate and simple lithographic techniques that permit the preparation of nanodevices. In this scenario, lithography based on Scanning Probe Microscopy (SPM) [1,2] has become very important due to its versatility, opening the door to new approaches such as the scratching or shaving of surfaces, the controlled deposition of material, or the realization of local chemical reactions. In particular, local oxidation nanolithography (LON) [3, 4, 5] a.k.a Local Anodic Oxidation (LAO) or Oxidation Scanning Probe Lithography (o-SPL), has been broadly used; under controlled ambient humidity conditions, when a bias voltage is applied between the tip of the microscope and the sample, a confined water meniscus is created by capillary condensation at the tip-surface interface. This confinement area acts as an electrochemical cell where an oxidation reaction takes place. The tip works as the cathode, the water acts as the electrolyte and the sample plays the role of the anode (oxidation reaction), so the chemical reaction gives rise to the formation of an oxide feature (see schematics at Figure 1a). The technique has been also extended to other liquids, which changes the nature of the patterned motifs, giving rise for example, to carbon-based features that can be used as etching resistant [6].  
Since the first nano-oxidation lithography performed on silicon by [PERSON] et al. in 1990 [PERSON] et al. (2010), a large number of materials have been lithographed with oxide motifs, i.e., metals, semiconductors, organic surfaces or layered crystals like Transition Metals Dichalcogenides (TMDCs) [7; 8; 9]. Thus, as a result of the interest awakened by the isolation of real 2D systems from bulk laminar crystals, LON was also extended to single layers with the formation of oxide patterns on graphene [10]. By means of this accurate lithography it is possible, for instance, to pattern graphene nanoribbons opening a band gap which permits the implementation of graphene in field effect transistors [11]. Regarding TMDCs, analogous nano-oxidation processes have been performed on semiconducting 2D-TMDCs, for example, by the selectively oxidation via oxygen plasma of MoS\({}_{2}\)[12] and by the laser-oxidation procedure of multilayer TaSe\({}_{2}\)[13] or WSe\({}_{2}\)[14]. However few examples can be found in the literature that use LON on ultrathin layers of TMDCs, namely the patterning of ultrathin metallic TaS\({}_{2}\) flakes [15], and the local oxidation of semiconducting MoS\({}_{2}\) layers [16]. Yet, the rich chemical tuneability and (opto)electronic properties that one can find within the TMDC family could provide new interesting platforms for the application of LON. Given the wide variety of applications that TMDCs have found nowadays in fields such as energy storage, optoelectronics, or biosensors [17; 18], LON could be a powerful tool to facilitate the structuration and integration of 2D crystals in devices or multifunctional systems. Interestingly, the ability to nanostructure thin superconducting TMDC layers by LON could be employed for the manipulation of the vortex state (in an attempt to modify the vortex pinning and to enhance the critical parameters, such as the critical current or the critical temperature) [19], and to address the appearance of novel vortex phases or the control of the vortices dynamics for developing new devices based on the flow of magnetic fluxons [20].  
In this scenario, we have performed a comprehensive study of the influence of different oxidation parameters that affect the LON process, such as the tip velocity or the tip-to-sample distance, using 2H-TaS\({}_{2}\) flakes as the target material. Additionally, we have also studied the oxidation process on other metallic systems (which are superconductors at low temperatures): 2H-TaSe\({}_{2}\), 2H-NbSe\({}_{2}\) and 2H-NbS\({}_{2}\); where we analyze the material-dependent oxidation patterns observed.