Q:

Get a parents + children tree with pg-promise

I use the pg-promise library with bluebird for making dependent queries. 
I have two tables, a and b, looking like this:
|   a   |     |   b   |  
|-------|     |-------|
| a_id  |     | b_id  |
| prop1 |     | prop2 |
              |  b_a  |

where b.b_a is a reference to a.a_id.  I want to select all entries matching a given prop1 and the result should contain all matching a-rows plus the corresponding b-rows for each a. This should be doable with two dependent queries.  Both queries may return multiple results. 
If table a only returns one row I can do this:
function getResult(prop1) {
    return db.task(function (t) {
        return t.one("select * from a where prop1=$1", prop1)
            .then(function (a) {
                return t.batch([a, t.any("select * from b where b_a=$1", a.a_id)]);
            })
            .then(function (data) {
                var a = data[0];
                var bs = data[1];
                bs.forEach(function (b) {
                    b.a = a;
                });
                return bs;
            });
    });
}

And I'm also able to get all matching b-entries for multiple a-results like this:
function getResult(prop1) {
    return db.task(function (t) {
        return t.many("select * from a where prop1=$1", prop1)
            .then(function (as) {
                var queries = [];
                as.forEach(function (a) {
                    queries.push(t.any("select * from b where b_a=$1", a.id));
                });
                return t.batch(queries); // could concat queries with as here, but there wouldn't be a reference which b row belongs to which a row
            })
            .then(function (data) {
                // data[n] contains all matching b rows
            });
    });
}

But how to bring those two together? 

A:

I am the author of pg-promise. 

When you have 2 tables: Parent -> Child with 1-to-many relationship, and you want to get an array of matching Parent rows, each row extended with property children set to an array of the corresponding rows from table Child ...
There are several ways to accomplish this, as the combination of pg-promise and promises in general is very flexible.  Here's the shortest version:
db.task(t => {
    return t.map('SELECT * FROM Parent WHERE prop1 = $1', [prop1], parent => {
        return t.any('SELECT * FROM Child WHERE parentId = $1', parent.id)
            .then(children => {
                parent.children = children;
                return parent;
            });
    }).then(t.batch) /* this is short for: data => t.batch(data) */
})
    .then(data => {
        /* data = the complete tree */
    });

This is what we do there:
First, we query for Parent items, then we map each row into a query for the corresponding Child items, which then sets its rows into the Parent and returns it.  Then we use method batch to resolve the array of Child queries returned from method map. 

The task will resolve with an array like this:
[
    {
        "parent1-prop1", "parent1-prop2",
        "children": [
            {"child1-prop1", "child1-prop2"},
            {"child2-prop1", "child2-prop2"}
        ]
    },
    {
        "parent2-prop1", "parent2-prop2",
        "children": [
            {"child3-prop1", "child3-prop2"},
            {"child4-prop1", "child4-prop2"}
        ]
    }    
]

API references: map, batch
UPDATE
See a better answer to this: JOIN table as array of results with PostgreSQL/NodeJS.