Split Time Trainer: Linda Rice Last race: Dec. 6, 6th Finish: 2nd by 3 1/4  Beyer: 63 Two-year-old New York-bred filly was off to a slow start but picked it up with a strong move around the turn and finished well for second behind an experienced rival in a promising debut. Runners from this barn routinely improve after a race, so look for her to be tough wherever she shows up next.   Nine Route Trainer: Jeremiah Englehart Last race: Dec. 8, 4th Finish: 1st by 6 ½ Beyer: 71 Two-year-old by The Factor switched to dirt to make the second start of his career off a layoff and improved significantly to leave a field of maidens behind with a strong finish, all after leaping up at the start to put himself out of position early.   My Boy Tate Trainer: Michelle Nevin Last race: Dec. 9, 6th Finish: 1st by 9 1/4  Beyer: 95 Made it 3 for 3 sprinting with a third consecutive blowout win and another Beyer top. He is out of New York-bred conditions now, but the lightly raced 3-year-old remains open to further improvement.