According to the Molinistic view, your repentance (asking for sins to be forgiven) was foreseen by God before all eternity, and was in his original plan. You are elected based on the foreknowledge of your merits (similar to Arminianism). This is called “middle knowledge”.
There is another view, called the Congruist, which is similar, but states that God gives the grace to those he has foreseen, due to their regeneracy, justification, estate in life, and myriad other factors, will indeed accept it, so that God’s sufficient grace is
always efficacious to those to whom it is given.
The Thomist-Bañezian position is more along the lines that your repentance is due to God’s working in your heart and your prior regeneration through the grace of God and the faith he has given you, and that you, as an unregenerate man, could never ask repentance. It’s “Catholic Calvinism”, or so I’ve heard it put (I believe Jimmy Akin said as much). It’s not that you were elected based on foreseen merits, but that any merit you appear to have, is based on your foreseen predestination/election.
When talking about falling from grace, the subject is a little trickier (councils have been held and books have been written to attempt to explain it); I would read the canons of the Second Council of Orange (not ecumenical, but highly influential), the canons on justification of the Ecumenical Council of Trent, the relevant parts of the
Summa Theologiae (mainly the articles of question 23, prima pars), and the book
Predestination by Dominican Father Reginald Garrigou-Lagrange, and the relevant parts of the Bible (Romans, especially).
Of course, those are what formed my views. I know William Lane Craig is a Molinist, I believe Alvin Plantinga is a Congruist (and they’re both Protestants). Suarez was the first Congruist. Molina the first Molinist. Thomas the first Thomist (elucidated by Bañez).
Catholic Encyclopedia has:
Thomism (in the “controversies on grace” article)
Molinism
Congruism