There are a couple ways to do this. Enabling trackers in the definition of \citetitle won't give you ibidem and shorthand abbreviations without some extra work. Just omitting labelname from \cite can make a (semantic) mess of some abbreviations - namely opcit, loccit and idem.
The code below (hopefully) takes care of these limitations by defining a hook to suppress labelname, author, or editor and fix problematic abbreviations. This hook can be used in the document body or within a definition of a command.
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[american]{babel}
\usepackage{csquotes}
\usepackage[style=verbose-trad1]{biblatex}
\addbibresource{biblatex-examples.bib}
\newbibmacro*{cite:full:noname}{%
\usebibmacro{cite:full:citepages}%
\printtext[bibhypertarget]{%
\usedriver
{\clearname{author}%
\clearname{editor}}
{\thefield{entrytype}}}%
\usebibmacro{shorthandintro}}
\newrobustcmd*{\citetitlehook}{%
\AtNextCite{%
\renewbibmacro*{cite:full}{\usebibmacro{cite:full:noname}}%
\renewbibmacro*{cite:name}{}%
\renewbibmacro*{cite:idem}{}%
\renewbibmacro*{cite:loccit}{\usebibmacro{cite:title}}%
\renewbibmacro*{cite:opcit}{\usebibmacro{cite:title}}}}
\renewrobustcmd*{\citetitle}{\citetitlehook\cite}
\newrobustcmd*{\citetitles}{\citetitlehook\cites}
\newrobustcmd*{\parencitetitle}{\citetitlehook\parencite}
\newrobustcmd*{\parencitetitles}{\citetitlehook\parencites}
\newrobustcmd*{\autocitetitle}{\citetitlehook\autocite}
\newrobustcmd*{\autocitetitles}{\citetitlehook\autocites}
\newrobustcmd*{\footcitetitle}{\citetitlehook\footcite}
\newrobustcmd*{\footcitetitles}{\citetitlehook\footcites}
\begin{document}
\null\vfill\noindent
Citetitle: \citetitle{kant:kpv}.
Parencitetitle: \parencite{kant:kpv}.
Autocitetitle.\autocitetitle[10]{companion}
Footcite with recurrent entry.\footcite[10]{companion}
Footcites with recurrent entry+page.\footcites{knuth:ct,knuth:ct:a}[10]{companion}
Footcite with recurrent author.\footcite{knuth:ct,knuth:ct:a}
Footcite with hook.\citetitlehook\footcite{augustine}
Footcite with hook and recurrent entry.\citetitlehook\footcite[10]{augustine}
Footcites with hook and recurrent entry+page.\citetitlehook\footcites{knuth:ct,knuth:ct:a}[10]{augustine}
Footcite with hook and recurrent author.\citetitlehook\footcite{knuth:ct,knuth:ct:a}
\end{document}

\footcitetitleworks fine, but\citetitlehookdoes not work if I want to cite inline. So I created another commmand called\citeonlytitleand... it worked! My question is: should\citetitlehookhave worked or is it a kind of "private command"? – Gastón Oct 20 '11 at 11:27\citetitlehookshould work in the document body. I'll revise the post to better demonstrate its range of use. – Audrey Oct 20 '11 at 14:03\citetitlehookdoesn't work in my document body. But\renewrobustcmd*{\citetitle}{\citetitlehook\cite}(or\newrobustcmd*{\citeonlytitle}{\citetitlehook\cite}) solves my problem. Thanks. – Gastón Oct 20 '11 at 15:10\citetitlehookdoesn't work in my actual document. I didn't test your example, but I will (could you post your .bib file?) – Gastón Oct 20 '11 at 15:43bibfile comes with thebiblatexdocumentation. You can find it indoc\latex\biblatex\examplesin yourtextree. – Audrey Oct 20 '11 at 16:05\citetitlehook: it doesn't work alone, but like a tool to switch the biblatex commands like\footcite. Sorry for the misunderstanding. New commands work fine with your example and my actual document. – Gastón Oct 20 '11 at 20:01