## 1 Introduction  
The anaerobic digestion of livestock effluents is considered valuable since it adds value to slurries since the process provides biogas (45-85% CH\({}_{4}\) and 25-50% CO\({}_{2}\)) as a renewable energy source and digestate with fertilising value to agricultural soils. The anaerobic digestion also contributes to the \"short carbon cycle\", ensuring carbon removal from the atmosphere. Thus, anaerobic digestion provides the carbon from the organic residues to produce biogas and continues with reusing the carbon contained in the digestate, putting it back in the soil. The whole carbon cycle is completed by valorising the carbon dioxide after producing biomethane, obtained after removing the carbon dioxide and trace gases from the biogas. The use of biogas and biomethane as renewable energy sources are essential to accelerate the reduction of GHG emissions (e.g., CO\({}_{2}\) and CH\({}_{4}\)), namely in agriculture and livestock activities, meet the renewable energy demand by 2030 and achieve climate targets in 2050 [1; 2; 3]. Europe is the largest producer of biogas and biomethane in the world today [4]. Globally in 2040, over 1000 Mtco of biomethane can be potentially produced, with average costs falling by 15% in relation to costs in 2018 [3; 4]. Therefore, the use of digestate as a biofertiliser will increase in the near future, contributing to the circular economy in agriculture, reducing demand for the carbon-intensive production of mineral fertilisers. The agronomic role of digestate is well recognised in several works in which its effect as a soil amendment increasing the level of the soil organic matter (SOM) [5; 6; 7] and also its role as a source of nutrients, namely N, P and K [8; 9; 10; 11] is reported. However, more profound knowledge is needed regarding the agronomic behaviour of digestates as a source of N to crops. In the EU, a low-cost and straightforward treatment of the digestate is widely used to achieve a solid/liquid (S/L) separation by press screw, allowing the production of two fractions with different characteristics. After S/L separation, the liquid fraction (LF) contain the majority of the total Kjeldahl nitrogen (TKN) of the digestate with values around 87% [12] and with an average content (\(n=11\)) of 97.5 g TKN kg\({}^{-1}\) DM which is mainly (61%) in the available N-NH\({}_{4}\) (TAN) mineral form [13]. These authors concluded that the LF could be used as a substitute for N mineral fertilisers, and the solid fraction (SF) can be proposed as an NP-organic fertiliser. They also observed high variability in the TKN and the TAN:TKN ratio of the solid fraction of the digestates reporting TKN values (\(n=13\)) between 124 and 73 g kg\({}^{-1}\) DM and TAN:TKN ratio values between 72 and 39%. Therefore, these results suggested that the SF can have a different ability to release N to crops, resulting from the proportion between their mineral and organic N forms.  
We hypothesised that the net N release to crops from the SF will be influenced not only by its content in mineral N (TAN:TKN ratio) but also by the TKN partition between mineral and organic forms causing differences in the balance between the immobilisation/mineralisation of the TKN.  
This work aimed to assess the fertilising value of two digestates with different NO:TKN ratios as organic amendments and as sources of N replacing N mineral fertilisers in a field experiment with two successive vegetable crops.